In mechanical and aeronautical engineering, degrees of freedom (DOF) describes flexibility of motion. A mechanism that has complete freedom of motion (even if only in a limited area, or envelope) has six degrees of freedom. Three modes are translation  the ability to move in each of three dimensions. Three are rotation, or the ability to change angle around three perpendicular axes.
To put it in simpler terms, each of the following is one degree: (1) Moving up and down; (2) moving left and right; (3) moving forward and back; (4) tilting up and down (pitching); (5) turning left and right (yawing); (6) tilting side to side (rolling). A mechanism that can (for instance) be raised and lowered, which has a pivoting head that can tilt forward or back, left or right, can be described as having 3 degrees of freedom (colloquially, 3DOF).
The concept of degrees of freedom is also used in statistics, in particular in the formulation of Pearson's chisquare test. See Analysis of variance for more.
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